1. Problems for Pencil and Paper The foundation of mathematics ...

We emphasize that the ability to do arithmetic with fractions by hand is important. It isnecessary for success in algebra; a skill with decimals but not fractions (for example, being ableto handle operations with fractions solely by means of a calculator) is not adequate. Indeed,fluency in the arithmetic of fractions is crucial background for developing fluency in the algebraof fractions. For fractions appear in algebra in the form of algebraic expressions that cannotbe treated as numbers on a calculator. Besides this, fractions play a key role in understandingstatistics and probability (and conversion of fractions to decimals makes its almost impossibleto trace an error or to easily assess how the answer will change if a problem is changed slightly).In the following problems we illustrate these skills.algebra and basic trigonometry of a similar flavor.We also include several problems in1:234 + 582 = 901 − 74 =582 × 7 = 392 ÷ 7 =Discussion: Prior to doing these calculations, students must be able to add and multiply onedigit numbers automatically (that is, without pencil and paper, and quickly, without the needto compute) with complete accuracy. They should also be able to do the inverse problems(subtraction, division, such as 16 − 9, 56 ÷ 8) automatically. The ability to do these basiccalculations automatically is fundamental for all that follows.2:357+ 842+ 2, 3923: Calculate 37 × 79. Then calculate 37 × .79.4: Calculate23| 805 and also 2.3| 8.055: Convert each of the following to a whole number, a proper fraction in lowest terms or amixed number with fractional part in lowest terms.2